This is a clinical research study of the safety and antiretroviral activity of an experimental HIV treatment drug called hydroxyurea in combination with two other anti-HIV drugs, ddI (didanosine, Videx) and d4T (stavudine, Zerit). Both ddI and d4T are FDA-approved for HIV treatment. The purpose of this study is to test the safety of nine regimens of hydroxyurea in combination with ddI and d4T in HIV-infected persons. Hydroxyurea is an investigational anti-HIV drug, but has been used in a large number of patients with sickle cell anemia at doses similar to those given in the study. The study will evaluate if hydroxyurea in combination with the other drugs decreases the amount of virus in the blood of HIV-infected persons. This study will also look at how hydroxyurea is absorbed into the body.